Finite Group Databasebeta

← #25963129

Subgroups — #25963129

Order 11008.

5126 conjugacy classes of subgroups.

The subgroup lattice has 1220 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063370C211yesmaximal, characteristic, complemented
2C2×#14583703C212yesmaximal, complemented
3#19148256C211yesmaximal, characteristic, complemented
4#19143900C214yesmaximal, complemented
5#19143898C212yesmaximal, complemented
6#19143864C212yesmaximal, complemented
7#19143858C214yesmaximal, complemented
8#19143849C211yesmaximal, characteristic, complemented
9#19143842C212yesmaximal, complemented
10#19143823C212yesmaximal, complemented
11#19143814C212yesmaximal, complemented
12#19143811C211yesmaximal, characteristic, complemented
13C2×#14583033C211yesmaximal, characteristic, complemented
14#447×D43C212yesmaximal, complemented
15#19143120C212yesmaximal, complemented
16#19143045C211yesmaximal, characteristic, complemented
17C43×#3003C211yesmaximal, characteristic, complemented
18C2×#13063371C2211yescharacteristic, complemented
19C2×#13063370—216no—
20C2×#13063370—21no—
21C2×#13063370—22no—
22C2×#13063370—21no—
23C2×#13063370C2212yes—
24C2×#13063370C2214yescomplemented
25C2×#13063370C2212yescomplemented
26C22×#10621898C2211yescharacteristic
27C22×#10621898C2211yescharacteristic, complemented
28C22×#10621900—21no—
29C22×#10621900C2212yescomplemented
30C23×C22⋊D43—22no—
31C22×D4×D43—21no—
32C22×D4×D43C2212yescomplemented
33#14583703—216no—
34C2×#13063353C2212yescomplemented
35C2×#13063352C2214yescomplemented
36C2×#13063349C2214yescomplemented
37C2×#13063346C2214yescomplemented
38C2×#13063345C2212yescomplemented
39C22×#10621882C2212yescomplemented
40C2×D8×D43C2214yescomplemented
41C2×#13063333C2212yescomplemented
42#14583570—21no—
43#14583558—21no—
44#14583545—21no—
45#14583541—22no—
46D4×D172—21no—
47#14583531—22no—
48#14583479C2212yescomplemented
49#14583477C2211yescharacteristic, complemented
50#14583468C2211yescharacteristic, complemented
51#14583465C2212yescomplemented
52#14583412C2212yescomplemented
53C2×#13063299C2211yescharacteristic, complemented
54#121×D43C2212yescomplemented
55#14583379C2211yescharacteristic, complemented
56#14583059C2212yescomplemented
57#14583058C2214yescomplemented
58#14583054C2211yescharacteristic, complemented
59#14583049C2211yescharacteristic, complemented
60#14583048C2214yescomplemented
61#14583046C2214yescomplemented
62#14583045C2214yescomplemented
63#14583045C2214yescomplemented
64#14583042C2212yescomplemented
65#14583041C2214yescomplemented
66#14583040C2212yescomplemented
67#14583037C2211yescharacteristic, complemented
68#14583035C2212yescomplemented
69#14583034C2214yescomplemented
70#14583034C2214yescomplemented
71#14583033C2212yescomplemented
72#14583033C2212yescomplemented
73#14583033C2214yescomplemented
74#14583032C2211yescharacteristic, complemented
75#14583031C2214yescomplemented
76#14582902C2214yescomplemented
77#14582901C2212yescomplemented
78#14582897C2214yescomplemented
79#14582893C2212yescomplemented
80#14582892C2214yescomplemented
81C2×#13063246C2212yescomplemented
82#102×D43C2214yescomplemented
83#14582867C2212yescomplemented
84#14582864C2214yescomplemented
85#14582861C2212yescomplemented
86C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
87C22⋊C8×D43C2212yescomplemented
88C23×D4×C43C2211yescharacteristic, complemented
89C2×AGL(1,ℤ/8)×C43C2212yescomplemented
90C43×#525C2211yescharacteristic, complemented
91C43×#450C2212yescomplemented
92C43×#450C2212yescomplemented
93C43×#447C2212yescomplemented
94C43×#447C2212yescomplemented
95C43×#418C2212yescomplemented
96C43×#407C2211yescharacteristic, complemented
97C24×D43—22no—
98#13063371—28no—
99#13063370—232no—
100#13063370—216no—
101#13063370—216no—
102#13063370—28no—
103#13063370—216no—
104#13063370—216no—
105#13063370—28no—
106#13063370—28no—
107#13063370D4116yescomplemented
108C2×#10621902C2312yescomplemented
109C2×#10621898—21no—
110C2×#10621898—21no—
111C2×#10621898—28no—
112C2×#10621898—28no—
113C2×#10621898—21no—
114C2×#10621898D411yescharacteristic
115C2×#10621898D412yes—
116C2×#10621898D411yescharacteristic
117C2×#10621898C2312yes—
118C2×#10621898C2311yescharacteristic
119C2×#10621898C2311yescharacteristic
120C2×#10621898C2312yes—
121C2×#10621898C2312yes—
122C2×#10621900—216no—
123C2×#10621900—216no—
124C2×#10621900—22no—
125C2×#10621900—22no—
126C2×#10621900—22no—
127C2×#10621900—24no—
128C2×#10621900—22no—
129C2×#10621900C2314yes—
130C2×#10621900C2314yes—
131C22×Dic86D411yescharacteristic
132C22×Dic86C2311yescharacteristic
133C22×D172—21no—
134C22×D172D411yescharacteristic
135C22×D172C2311yescharacteristic
136C22×D172C2311yescharacteristic, complemented
137C22×C22⋊D43—232no—
138C22×C22⋊D43—21no—
139C22×C22⋊D43—22no—
140C22×C22⋊D43—24no—
141C22×C22⋊D43—24no—
142C22×C22⋊D43—24no—
143C22×C22⋊D43—24no—
144C22×C22⋊D43—21no—
145C22×C22⋊D43—22no—
146C22×C22⋊D43D412yes—
147C2×D4×D43—216no—
148C2×D4×D43—216no—
149C2×D4×D43—22no—
150C2×D4×D43—22no—
151C2×D4×D43—22no—
152C2×D4×D43—24no—
153C2×D4×D43—22no—
154C2×D4×D43—22no—
155C2×D4×D43—22no—
156C2×D4×D43C2314yes—
157C2×D4×D43C2314yes—
158C2×D4×D43C2312yescomplemented
159C23×Dic43—22no—
160C22×C4×D43—21no—
161C22×C4×D43C2312yes—
162#13063353—28no—
163#13063352—216no—
164#13063349—216no—
165#13063346—216no—
166#13063345—28no—
167C2×#10621885C2312yescomplemented
168C2×#10621873C2314yescomplemented
169C2×#10621883C2312yescomplemented
170C2×#10621884C2312yescomplemented
171C2×D344C2314yescomplemented
172C2×#10621882—28no—
173C2×#10621882C2312yescomplemented
174C2×#10621882C2314yescomplemented
175C2×#10621882C2314yescomplemented
176D8×D43—216no—
177#13063333—28no—
178C2×#10621872C2314yescomplemented
179C22×C43⋊C8C2312yescomplemented
180C2×C8×D43C2314yescomplemented
181#13063322—21no—
182#13063321—22no—
183#13063313—21no—
184#13063311—22no—
185#13063310—22no—
186#13063304—21no—
187#13063303—22no—
188#13063301C2312yescomplemented
189#13063300—22no—
190#13063300C2312yescomplemented
191#13063300C2312yescomplemented
192#13063299—21no—
193#13063299—21no—
194#13063299—21no—
195#13063299C2312yes—
196#13063299C2312yescomplemented
197#13063298—22no—
198#13063298—22no—
199#13063298—22no—
200#13063297—22no—
201#13063297—22no—
202#13063296C2312yescomplemented
203#13063295—22no—
204#13063295—22no—
205#13063295—22no—
206#13063293—22no—
207C4×Dic86—21no—
208C4×D172—21no—
209#13063287—22no—
210(C22⋊D43)⋊C4—22no—
211(C22⋊D43)⋊C4—22no—
212#13063283C2312yescomplemented
213C2×C4⋊Dic43C2311yescharacteristic, complemented
214C4⋊C4×D43C2312yescomplemented
215C2×(C2×D43)⋊C4—21no—
216C22⋊C4×D43—22no—
217#13063250C2314yescomplemented
218#13063248C2312yescomplemented
219#13063248C2312yescomplemented
220#13063247C2314yescomplemented
221#13063246C2314yescomplemented
222#13063246C2314yescomplemented
223#13063245C2312yescomplemented
224#13063245C2312yescomplemented
225C22⋊(C43⋊C8)C2311yescharacteristic
226C22⋊(C43⋊C8)C2311yescharacteristic
227C22⋊(C43⋊C8)C2312yescomplemented
228(C2×D43)⋊C8C2314yescomplemented
229(C2×D43)⋊C8C2314yescomplemented
230C25×C43—21no—
231C2×#41×C43C2311yescharacteristic, complemented
232C22×D4×C43—28no—
233C22×D4×C43—21no—
234C22×D4×C43—21no—
235C22×D4×C43—21no—
236C22×D4×C43C2312yes—
237C22×D4×C43C2312yes—
238C22×D4×C43C2312yes—
239C23×C4×C43C2311yescharacteristic
240AGL(1,ℤ/8)×C43—28no—
241C2×SD16×C43C2314yescomplemented
242C2×D8×C43C2314yescomplemented
243C2×M16×C43C2312yescomplemented
244#123×C43—21no—
245C22⋊Q8×C43C2311yescharacteristic
246C22⋊Q8×C43C2311yescharacteristic, complemented
247#121×C43C2311yescharacteristic
248#121×C43C2311yescharacteristic, complemented
249#120×C43—21no—
250C4×D4×C43—21no—
251C4×D4×C43—21no—
252#117×C43C2311yescharacteristic, complemented
253#102×C43C2314yescomplemented
254#102×C43C2314yescomplemented
255C22⋊C8×C43C2312yes—
256C22⋊C8×C43C2312yescomplemented
257C24×C43—28no—
258C24×C43—22no—
259C24×C43—22no—
260C24×C43—22no—
261C24×C43—82no—
262C24×C43—82no—
263C24×C43C2×D411yescharacteristic
264C23×D43—21no—
265C23×D43—216no—
266C23×D43—24no—
267C23×D43—24no—
268C23×D43—21no—
269C23×D43—22no—
270C23×D43—84no—
271C23×D43—84no—
272C23×D43C2×D412yes—
273#41×C43—24no—
274C2×Q8×C43C2411yescharacteristic
275C2×D4×C43—28no—
276C2×D4×C43—28no—
277C2×D4×C43—28no—
278C2×D4×C43—28no—
279C2×D4×C43—28no—
280C2×D4×C43—22no—
281C2×D4×C43—22no—
282C2×D4×C43—22no—
283C2×D4×C43—24no—
284C2×D4×C43—21no—
285C2×D4×C43—21no—
286C2×D4×C43—21no—
287C2×D4×C43C2×D418yescomplemented
288C2×D4×C43C2411yescharacteristic
289C2×D4×C43C2414yes—
290C22×C4×C43—24no—
291C22×C4×C43—21no—
292C22×C4×C43C2×D411yescharacteristic
293C22×C4×C43C2×D411yescharacteristic
294C22×C4×C43C2×D411yescharacteristic
295C22×C4×C43C2411yescharacteristic
296C22×C4×C43C2411yescharacteristic
297C22×C4×C43C2411yescharacteristic
298C2×C22⋊D43—216no—
299C2×C22⋊D43—216no—
300C2×C22⋊D43—28no—
301C2×C22⋊D43—232no—
302C2×C22⋊D43—232no—
303C2×C22⋊D43—232no—
304C2×C22⋊D43—28no—
305C2×C22⋊D43—232no—
306C2×C22⋊D43—24no—
307C2×C22⋊D43—24no—
308C2×C22⋊D43—22no—
309C2×C22⋊D43—22no—
310C2×C22⋊D43—22no—
311C2×C22⋊D43—22no—
312C2×C22⋊D43—22no—
313C2×C22⋊D43—24no—
314C2×C22⋊D43—24no—
315C2×C22⋊D43—22no—
316C2×C22⋊D43—82no—
317C2×C22⋊D43C2×D412yes—
318C2×C22⋊D43C2×D412yes—
319C2×C22⋊D43C2×D412yes—
320C2×C22⋊D43C2×D412yes—
321C22×Dic43—216no—
322C22×Dic43—24no—
323C22×Dic43—24no—
324C22×Dic43—21no—
325C22×Dic43—21no—
326C22×Dic43C2×D412yes—
327#10621902—28no—
328#10621900—216no—
329#10621900—216no—
330#10621900—216no—
331#10621900—232no—
332#10621900—28no—
333#10621900—28no—
334#10621900—216no—
335#10621900—28no—
336#10621900C2×D4116yescomplemented
337D4×D43—216no—
338D4×D43—216no—
339D4×D43—232no—
340D4×D43—216no—
341D4×D43—28no—
342D4×D43—216no—
343D4×D43—28no—
344D4×D43—28no—
345D4×D43—28no—
346D4×D43—48no—
347D4×D43—84no—
348D4×D43C2×D4116yescomplemented
349#10621898—28no—
350#10621898—28no—
351#10621898—24no—
352#10621898—24no—
353#10621898—28no—
354#10621898—24no—
355#10621898—24no—
356#10621898—28no—
357#10621898—24no—
358#10621898—24no—
359#10621898—44no—
360#10621898C2×D418yes—
361#10621898C2×D418yescomplemented
362C2×D172—21no—
363C2×D172—24no—
364C2×D172—24no—
365C2×D172—21no—
366C2×D172—22no—
367C2×D172—22no—
368C2×D172—22no—
369C2×D172—24no—
370C2×D172—44no—
371C2×D172C2×D412yes—
372C2×D172C2×D411yescharacteristic
373C2×D172C2×D411yescharacteristic
374C2×D172C2412yes—
375C2×D172C2412yes—
376C2×C4×D43—28no—
377C2×C4×D43—22no—
378C2×C4×D43—22no—
379C2×C4×D43—28no—
380C2×C4×D43—22no—
381C2×C4×D43—22no—
382C2×C4×D43C2×D412yes—
383C2×C4×D43C2×D412yes—
384C2×C4×D43C2412yes—
385C2×C4×D43C2412yes—
386C2×Dic86—21no—
387C2×Dic86—24no—
388C2×Dic86—24no—
389C2×Dic86C2×D412yes—
390C2×Dic86C2×D411yescharacteristic
391C2×Dic86C2×D411yescharacteristic
392C2×Dic86C2412yes—
393SD16×C43—28no—
394D8×C43—28no—
395M16×C43—24no—
396C2×C8×C43C2414yes—
397C4⋊C4×C43—21no—
398C4⋊C4×C43—21no—
399C4⋊C4×C43C2411yescharacteristic
400C4⋊C4×C43C2411yescharacteristic
401C22⋊C4×C43—21no—
402C22⋊C4×C43—21no—
403C22⋊C4×C43—21no—
404C22⋊C4×C43—21no—
405C22⋊C4×C43—21no—
406C42×C43—21no—
407C22⋊Dic43—22no—
408#10621885—24no—
409#10621884—24no—
410#10621883—24no—
411#10621882—28no—
412#10621882—28no—
413#10621882—24no—
414(C2×D43)⋊C4—22no—
415(C2×D43)⋊C4—22no—
416(C2×D43)⋊C4—22no—
417(C2×D43)⋊C4—22no—
418(C2×D43)⋊C4—22no—
419(C2×D43)⋊C4—22no—
420C4⋊Dic43—21no—
421C4⋊Dic43C2412yes—
422Dic43⋊C4—22no—
423Dic43⋊C4—22no—
424C4×Dic43—22no—
425C2×C43⋊C8—24no—
426C2×C43⋊C8C2412yes—
427C2×C43⋊C8C2412yes—
428D344—28no—
429#10621873—28no—
430#10621872—28no—
431C8×D43—28no—
432C23×C43—28no—
433C23×C43—28no—
434C23×C43—22no—
435C23×C43—22no—
436C23×C43—24no—
437C23×C43—28no—
438C23×C43—21no—
439C23×C43—41no—
440C23×C43—44no—
441C23×C43—44no—
442C23×C43—82no—
443C23×C43—82no—
444C23×C43—82no—
445C23×C43—82no—
446C23×C43—816no—
447C23×C43C22×D411yescharacteristic
448C23×C43C22×D411yescharacteristic
449C23×C43C22×D411yescharacteristic
450C22×D43—24no—
451C22×D43—24no—
452C22×D43—22no—
453C22×D43—216no—
454C22×D43—24no—
455C22×D43—216no—
456C22×D43—22no—
457C22×D43—42no—
458C22×D43—42no—
459C22×D43—42no—
460C22×D43—42no—
461C22×D43—44no—
462C22×D43—84no—
463C22×D43—84no—
464C22×D43—84no—
465C22×D43—84no—
466C22×D43—82no—
467C22×D43—82no—
468C22×D43—832no—
469C22×D43—81no—
470C22×D43—81no—
471C22×D43C22×D412yes—
472C22×D43C22×D412yes—
473Q8×C43—22no—
474D4×C43—28no—
475D4×C43—28no—
476D4×C43—28no—
477D4×C43—24no—
478D4×C43—22no—
479D4×C43—42no—
480D4×C43—42no—
481D4×C43—81no—
482D4×C43C22×D418yes—
483C2×C4×C43—22no—
484C2×C4×C43—22no—
485C2×C4×C43—22no—
486C2×C4×C43—22no—
487C2×C4×C43—22no—
488C2×C4×C43—21no—
489C2×C4×C43—21no—
490C2×C4×C43—21no—
491C2×C4×C43—42no—
492C2×C4×C43C22×D411yescharacteristic
493C2×C4×C43C22×D411yescharacteristic
494C2×C4×C43C22×D411yescharacteristic
495C2×C4×C43C22×D414yes—
496C2×C4×C43C2511yescharacteristic
497C22⋊D43—28no—
498C22⋊D43—216no—
499C22⋊D43—216no—
500C22⋊D43—24no—
501C22⋊D43—28no—
502C22⋊D43—24no—
503C22⋊D43—216no—
504C22⋊D43—24no—
505C22⋊D43—216no—
506C22⋊D43—44no—
507C22⋊D43—44no—
508C22⋊D43—82no—
509C22⋊D43—82no—
510C22⋊D43#12018yes—
511C2×Dic43—24no—
512C2×Dic43—216no—
513C2×Dic43—22no—
514C2×Dic43—24no—
515C2×Dic43—216no—
516C2×Dic43—22no—
517C2×Dic43—81no—
518C2×Dic43C22×D412yes—
519C2×Dic43C22×D412yes—
520D172—24no—
521D172—24no—
522D172—22no—
523D172—22no—
524D172—24no—
525D172—44no—
526D172—42no—
527D172—82no—
528D172—82no—
529D172#12014yes—
530D172C22×D414yes—
531C4×D43—28no—
532C4×D43—24no—
533C4×D43—28no—
534C4×D43—24no—
535C4×D43—24no—
536C4×D43—44no—
537C4×D43—82no—
538C4×D43C22×D418yes—
539Dic86—24no—
540Dic86—22no—
541Dic86—22no—
542Dic86—24no—
543Dic86#12014yes—
544Dic86C22×D414yes—
545C8×C43—24no—
546C43⋊C8—22no—
547C43⋊C8—22no—
548#60372—431nomaximal, Sylow
549C22×C43—21no—
550C22×C43—21no—
551C22×C43—21no—
552C22×C43—21no—
553C22×C43—21no—
554C22×C43—28no—
555C22×C43—21no—
556C22×C43—21no—
557C22×C43—44no—
558C22×C43—416no—
559C22×C43—44no—
560C22×C43—44no—
561C22×C43—41no—
562C22×C43—41no—
563C22×C43—41no—
564C22×C43—88no—
565C22×C43—88no—
566C22×C43C2×#12012yes—
567C22×C43#57612yescomplemented
568C22×C43C23×D411yescharacteristic
569C2×D43—22no—
570C2×D43—22no—
571C2×D43—22no—
572C2×D43—24no—
573C2×D43—22no—
574C2×D43—22no—
575C2×D43—48no—
576C2×D43—48no—
577C2×D43—42no—
578C2×D43—42no—
579C2×D43—42no—
580C2×D43—42no—
581C2×D43—42no—
582C2×D43—816no—
583C2×D43—816no—
584C2×D43—164no—
585C2×D43—162no—
586C2×D43C2×#12014yes—
587C4×C43—21no—
588C4×C43—21no—
589C4×C43—41no—
590C4×C43—41no—
591C4×C43—41no—
592C4×C43C2×#12012yes—
593C4×C43C23×D412yes—
594Dic43—22no—
595Dic43—24no—
596Dic43—42no—
597Dic43C2×#12014yes—
598C22×H(5,𝔽2)—431no—
599C2×#576—432no—
600#3488—431no—
601#3012—434no—
602#3012—432no—
603#3008—434no—
604#3008—432no—
605#3006—432no—
606#3006—431no—
607#3003—432no—
608#3003D4311yescharacteristic, complemented
609#3002—432no—
610#3002—431no—
611C2×#447—432no—
612C2×#447—431no—
613#2897—432no—
614#2880—431no—
615C2×C43—22no—
616C2×C43—22no—
617C2×C43—48no—
618C2×C43—41no—
619C2×C43—81no—
620C2×C43C22×#12011yescharacteristic
621C2×C43C2×#57611yescharacteristic
622C2×C43#358511yescharacteristic
623D43—24no—
624D43—42no—
625D43—44no—
626D43—82no—
627C2×H(5,𝔽2)—431no—
628C2×H(5,𝔽2)—432no—
629C2×H(5,𝔽2)—434no—
630C2×H(5,𝔽2)—432no—
631C2×H(5,𝔽2)—862no—
632C2×H(5,𝔽2)—861no—
633C2×H(5,𝔽2)—861no—
634C2×H(5,𝔽2)—8616no—
635C22×#41—431no—
636C22×#41—432no—
637C22×#41—431no—
638C22×#41—861no—
639C23×D4—432no—
640C23×D4—861no—
641C23×D4—862no—
642C23×D4C2×D4311yescharacteristic, complemented
643#576—8616no—
644C2×AGL(1,ℤ/8)—434no—
645C2×AGL(1,ℤ/8)—434no—
646C2×AGL(1,ℤ/8)—432no—
647C2×AGL(1,ℤ/8)C2×D4312yescomplemented
648C2×#135—432no—
649C2×#135—434no—
650C22×D8—432no—
651C22×D8—434no—
652C2×#131—432no—
653#550—861no—
654#548—861no—
655#546—861no—
656#546—862no—
657D42—861no—
658D42—862no—
659#537—431no—
660#537—432no—
661#535—432no—
662#535—431no—
663#525—432no—
664#525C2×D4311yescharacteristic, complemented
665C2×#121—431no—
666C2×#121—432no—
667#520—431no—
668#452—434no—
669#452—432no—
670#451—431no—
671#450—434no—
672#450—431no—
673#450C2×D4312yescomplemented
674#450C2×D4312yescomplemented
675#449—434no—
676#449—432no—
677#449—434no—
678#449—434no—
679#449—434no—
680#448—431no—
681#448—432no—
682#447—432no—
683#447—432no—
684#447—434no—
685#447—434no—
686#447—431no—
687#447—434no—
688#447—434no—
689#447—432no—
690#447C2×D4312yescomplemented
691#447C2×D4312yescomplemented
692#418—434no—
693#418C2×D4312yescomplemented
694#417—432no—
695#417—434no—
696#416—432no—
697#416—434no—
698C2×#102—432no—
699C2×#102—434no—
700#408—432no—
701#408—434no—
702#407—432no—
703#407C2×D4311yescharacteristic, complemented
704C2×C22⋊C8—431no—
705C2×C22⋊C8—432no—
706C43#6037211yescharacteristic, complemented, Sylow
707C25—21no—
708C25—862no—
709H(5,𝔽2)—4316no—
710H(5,𝔽2)—8616no—
711H(5,𝔽2)—8616no—
712H(5,𝔽2)—868no—
713H(5,𝔽2)—868no—
714H(5,𝔽2)—8616no—
715H(5,𝔽2)—8632no—
716H(5,𝔽2)—8616no—
717H(5,𝔽2)—868no—
718H(5,𝔽2)—868no—
719C2×#41—431no—
720C2×#41—432no—
721C2×#41—431no—
722C2×#41—431no—
723C2×#41—432no—
724C2×#41—431no—
725C2×#41—432no—
726C2×#41—434no—
727C2×#41—434no—
728C2×#41—432no—
729C2×#41—432no—
730C2×#41—861no—
731C2×#41—868no—
732C2×#41—868no—
733C2×#41—862no—
734C2×#41—862no—
735C2×#41—862no—
736C2×#41—864no—
737C2×#41—862no—
738C2×#41—8616no—
739C2×#41—8616no—
740C2×#41—861no—
741C2×#41—861no—
742C2×#41C22×D4311yescharacteristic, complemented
743C22×Q8—431no—
744C22×Q8—431no—
745C22×D4—28no—
746C22×D4—21no—
747C22×D4—21no—
748C22×D4—21no—
749C22×D4—434no—
750C22×D4—432no—
751C22×D4—432no—
752C22×D4—434no—
753C22×D4—431no—
754C22×D4—431no—
755C22×D4—431no—
756C22×D4—861no—
757C22×D4—862no—
758C22×D4—862no—
759C22×D4—862no—
760C22×D4—8616no—
761C22×D4—862no—
762C22×D4—864no—
763C22×D4—862no—
764C22×D4—862no—
765C22×D4—8616no—
766C22×D4—862no—
767C22×D4—864no—
768C22×D4—864no—
769C22×D4—864no—
770C22×D4—864no—
771C22×D4—862no—
772C22×D4—8632no—
773C22×D4—861no—
774C22×D4—861no—
775C22×D4C22×D4312yes—
776C22×D4C22×D4312yes—
777C22×D4C22×D4312yes—
778C23×C4—432no—
779C23×C4—862no—
780C23×C4—861no—
781C23×C4C22×D4311yescharacteristic
782AGL(1,ℤ/8)—28no—
783AGL(1,ℤ/8)—868no—
784AGL(1,ℤ/8)—8616no—
785AGL(1,ℤ/8)—8616no—
786#135—8616no—
787#135—868no—
788C2×Q16—432no—
789C2×SD16—432no—
790C2×SD16—432no—
791C2×SD16—434no—
792C2×SD16C22×D4314yescomplemented
793C2×D8—432no—
794C2×D8—434no—
795C2×D8—434no—
796C2×D8—434no—
797C2×D8—8616no—
798C2×D8—868no—
799C2×D8C22×D4314yescomplemented
800#131—868no—
801C2×M16—434no—
802C2×M16C22×D4312yescomplemented
803C22×C8—432no—
804C22×C8—434no—
805#127—861no—
806#127—862no—
807#124—861no—
808#124—862no—
809#123—21no—
810#123—862no—
811C22⋊Q8—432no—
812C22⋊Q8—862no—
813C22⋊Q8—861no—
814C22⋊Q8C22×D4311yescharacteristic
815C22⋊Q8C22×D4311yescharacteristic, complemented
816#121—432no—
817#121—432no—
818#121—432no—
819#121—432no—
820#121—432no—
821#121—862no—
822#121—862no—
823#121—862no—
824#121—862no—
825#121—861no—
826#121—862no—
827#121—862no—
828#121—861no—
829#121—861no—
830#121C22×D4311yescharacteristic
831#121C22×D4311yescharacteristic, complemented
832#120—21no—
833#120—862no—
834#120—862no—
835#120—862no—
836#120—862no—
837C4×Q8—861no—
838C4×D4—21no—
839C4×D4—21no—
840C4×D4—861no—
841C4×D4—862no—
842C4×D4—862no—
843C4×D4—862no—
844#117—432no—
845#117C22×D4311yescharacteristic, complemented
846C2×C4⋊C4—431no—
847C2×C4⋊C4—432no—
848C2×C22⋊C4—862no—
849C2×C22⋊C4—861no—
850#103—434no—
851#103—432no—
852#103—432no—
853#102—434no—
854#102—434no—
855#102—434no—
856#102—432no—
857#102—432no—
858#102C22×D4314yescomplemented
859#102C22×D4314yescomplemented
860C22⋊C8—431no—
861C22⋊C8—431no—
862C22⋊C8—432no—
863C22⋊C8—434no—
864C22⋊C8—434no—
865C22⋊C8C22×D4312yes—
866C22⋊C8C22×D4312yescomplemented
867C24—28no—
868C24—22no—
869C24—22no—
870C24—22no—
871C24—82no—
872C24—82no—
873C24—432no—
874C24—864no—
875C24—864no—
876C24—862no—
877C24—8616no—
878C24—861no—
879C24—861no—
880C24—3444no—
881C24—3444no—
882C24D4×D4311yescharacteristic
883#41—24no—
884#41—438no—
885#41—4316no—
886#41—438no—
887#41—868no—
888#41—868no—
889#41—864no—
890#41—864no—
891#41—864no—
892#41—864no—
893#41—868no—
894#41—868no—
895#41—868no—
896#41—868no—
897#41—868no—
898#41—8616no—
899#41—8616no—
900#41—8616no—
901#41—8632no—
902#41—8616no—
903#41—868no—
904#41—864no—
905#41—864no—
906#41—1724no—
907C2×Q8—431no—
908C2×Q8—432no—
909C2×Q8—431no—
910C2×Q8—432no—
911C2×Q8—864no—
912C2×Q8—864no—
913C2×Q8—861no—
914C2×Q8C23×D4311yescharacteristic
915C2×D4—28no—
916C2×D4—28no—
917C2×D4—28no—
918C2×D4—28no—
919C2×D4—28no—
920C2×D4—21no—
921C2×D4—21no—
922C2×D4—21no—
923C2×D4—22no—
924C2×D4—22no—
925C2×D4—22no—
926C2×D4—24no—
927C2×D4—432no—
928C2×D4—4316no—
929C2×D4—432no—
930C2×D4—432no—
931C2×D4—432no—
932C2×D4—431no—
933C2×D4—432no—
934C2×D4—431no—
935C2×D4—432no—
936C2×D4—432no—
937C2×D4—864no—
938C2×D4—864no—
939C2×D4—862no—
940C2×D4—862no—
941C2×D4—862no—
942C2×D4—868no—
943C2×D4—868no—
944C2×D4—864no—
945C2×D4—864no—
946C2×D4—862no—
947C2×D4—868no—
948C2×D4—8616no—
949C2×D4—8616no—
950C2×D4—8616no—
951C2×D4—8632no—
952C2×D4—8616no—
953C2×D4—868no—
954C2×D4—8632no—
955C2×D4—864no—
956C2×D4—864no—
957C2×D4—8616no—
958C2×D4—8616no—
959C2×D4—868no—
960C2×D4—8632no—
961C2×D4—8632no—
962C2×D4—8632no—
963C2×D4—862no—
964C2×D4—862no—
965C2×D4—868no—
966C2×D4—862no—
967C2×D4—862no—
968C2×D4—862no—
969C2×D4—861no—
970C2×D4—864no—
971C2×D4—861no—
972C2×D4—3444no—
973C2×D4—3442no—
974C2×D4—1724no—
975C2×D4—1728no—
976C2×D4D4×D4318yescomplemented
977C2×D4C23×D4311yescharacteristic
978C2×D4C23×D4314yes—
979C22×C4—24no—
980C22×C4—21no—
981C22×C4—432no—
982C22×C4—432no—
983C22×C4—432no—
984C22×C4—432no—
985C22×C4—432no—
986C22×C4—868no—
987C22×C4—862no—
988C22×C4—868no—
989C22×C4—862no—
990C22×C4—864no—
991C22×C4—864no—
992C22×C4—8616no—
993C22×C4—861no—
994C22×C4—862no—
995C22×C4—862no—
996C22×C4—861no—
997C22×C4D4×D4311yescharacteristic
998C22×C4D4×D4311yescharacteristic
999C22×C4D4×D4311yescharacteristic
1000C22×C4C23×D4311yescharacteristic
1001C22×C4C23×D4311yescharacteristic
1002C22×C4C23×D4311yescharacteristic
1003Q16—864no—
1004SD16—28no—
1005SD16—868no—
1006SD16—864no—
1007SD16—864no—
1008D8—28no—
1009D8—868no—
1010D8—864no—
1011D8—868no—
1012D8—868no—
1013M16—24no—
1014M16—868no—
1015C2×C8—432no—
1016C2×C8—432no—
1017C2×C8—868no—
1018C2×C8—864no—
1019C2×C8C23×D4314yes—
1020C4⋊C4—21no—
1021C4⋊C4—21no—
1022C4⋊C4—432no—
1023C4⋊C4—862no—
1024C4⋊C4—862no—
1025C4⋊C4—861no—
1026C4⋊C4C23×D4311yescharacteristic
1027C4⋊C4C23×D4311yescharacteristic
1028C22⋊C4—21no—
1029C22⋊C4—21no—
1030C22⋊C4—21no—
1031C22⋊C4—21no—
1032C22⋊C4—21no—
1033C22⋊C4—862no—
1034C22⋊C4—862no—
1035C22⋊C4—862no—
1036C22⋊C4—862no—
1037C22⋊C4—862no—
1038C22⋊C4—862no—
1039C22⋊C4—862no—
1040C42—21no—
1041C42—862no—
1042C23—28no—
1043C23—28no—
1044C23—22no—
1045C23—22no—
1046C23—24no—
1047C23—28no—
1048C23—21no—
1049C23—41no—
1050C23—44no—
1051C23—44no—
1052C23—82no—
1053C23—82no—
1054C23—82no—
1055C23—82no—
1056C23—816no—
1057C23—432no—
1058C23—432no—
1059C23—8616no—
1060C23—864no—
1061C23—8616no—
1062C23—864no—
1063C23—864no—
1064C23—862no—
1065C23—862no—
1066C23—3441no—
1067C23—3441no—
1068C23—3444no—
1069C23—3444no—
1070C23—3444no—
1071C23—3444no—
1072C23—3442no—
1073C23—3442no—
1074C23—34432no—
1075C23—1722no—
1076C23—1722no—
1077C23—1724no—
1078C23—1722no—
1079C23—1722no—
1080C23C2×D4×D4311yescharacteristic
1081C23C2×D4×D4311yescharacteristic
1082C23C2×D4×D4311yescharacteristic
1083Q8—22no—
1084Q8—434no—
1085Q8—434no—
1086Q8—864no—
1087Q8—864no—
1088Q8—862no—
1089Q8—862no—
1090D4—28no—
1091D4—28no—
1092D4—28no—
1093D4—24no—
1094D4—22no—
1095D4—42no—
1096D4—42no—
1097D4—81no—
1098D4—438no—
1099D4—434no—
1100D4—434no—
1101D4—864no—
1102D4—864no—
1103D4—864no—
1104D4—8616no—
1105D4—864no—
1106D4—8616no—
1107D4—8616no—
1108D4—868no—
1109D4—8616no—
1110D4—864no—
1111D4—868no—
1112D4—862no—
1113D4—862no—
1114D4—864no—
1115D4—3442no—
1116D4—3442no—
1117D4—3442no—
1118D4—3442no—
1119D4—1724no—
1120D4—1724no—
1121D4—1724no—
1122D4—1722no—
1123D4C2×D4×D4318yes—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—42no—
1133C2×C4—432no—
1134C2×C4—438no—
1135C2×C4—432no—
1136C2×C4—864no—
1137C2×C4—864no—
1138C2×C4—868no—
1139C2×C4—864no—
1140C2×C4—8616no—
1141C2×C4—864no—
1142C2×C4—8616no—
1143C2×C4—862no—
1144C2×C4—868no—
1145C2×C4—864no—
1146C2×C4—862no—
1147C2×C4—3442no—
1148C2×C4—3441no—
1149C2×C4—1724no—
1150C2×C4C2×D4×D4311yescharacteristic
1151C2×C4C2×D4×D4311yescharacteristic
1152C2×C4C2×D4×D4311yescharacteristic
1153C2×C4C2×D4×D4314yes—
1154C2×C4C24×D4311yescharacteristic
1155C8—24no—
1156C8—862no—
1157C8—862no—
1158C22—21no—
1159C22—21no—
1160C22—21no—
1161C22—21no—
1162C22—21no—
1163C22—28no—
1164C22—21no—
1165C22—21no—
1166C22—44no—
1167C22—416no—
1168C22—44no—
1169C22—44no—
1170C22—41no—
1171C22—41no—
1172C22—41no—
1173C22—88no—
1174C22—88no—
1175C22—434no—
1176C22—862no—
1177C22—862no—
1178C22—864no—
1179C22—862no—
1180C22—862no—
1181C22—862no—
1182C22—34416no—
1183C22—34416no—
1184C22—1728no—
1185C22—1728no—
1186C22—1722no—
1187C22—1722no—
1188C22—1722no—
1189C22—1722no—
1190C22—1722no—
1191C22—6882no—
1192C22—6884no—
1193C22#120×D4312yes—
1194C22#1458370312yescomplemented
1195C22C22×D4×D4311yescharacteristic
1196C4—21no—
1197C4—21no—
1198C4—41no—
1199C4—41no—
1200C4—41no—
1201C4—434no—
1202C4—862no—
1203C4—864no—
1204C4—1722no—
1205C4#120×D4312yes—
1206C4C22×D4×D4312yes—
1207C2—22no—
1208C2—22no—
1209C2—41no—
1210C2—48no—
1211C2—81no—
1212C2—864no—
1213C2—3442no—
1214C2—1722no—
1215C2—1724no—
1216C2C2×#120×D4311yescharacteristic
1217C2C2×#1458370311yescharacteristic
1218C2#1914937111yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3003C2
socleC22×C43C23×D4
hypercenter#3003D43
hypocenterC43#60372
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3003

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×#13063370C2semidirect
2. C2×#14583703C2semidirect
3. #19148256C2semidirect
4. #19143900C2semidirect
5. #19143898C2semidirect
6. #19143864C2semidirect
7. #19143858C2semidirect
8. #19143849C2semidirect
9. #19143842C2semidirect
10. #19143823C2semidirect
11. #19143814C2semidirect
12. #19143811C2semidirect
13. C2×#14583033C2semidirect
14. #447×D43C2semidirect
15. #19143120C2semidirect
16. #19143045C2semidirect
17. C43×#3003C2semidirect
18. C2×#13063371C22semidirect
24. C2×#13063370C22semidirect
25. C2×#13063370C22semidirect
27. C22×#10621898C22semidirect
29. C22×#10621900C22semidirect
32. C22×D4×D43C22semidirect
34. C2×#13063353C22semidirect
35. C2×#13063352C22semidirect
36. C2×#13063349C22semidirect
37. C2×#13063346C22semidirect
38. C2×#13063345C22semidirect
39. C22×#10621882C22semidirect
40. C2×D8×D43C22semidirect
41. C2×#13063333C22semidirect
48. #14583479C22semidirect
49. #14583477C22semidirect
50. #14583468C22semidirect
51. #14583465C22semidirect
52. #14583412C22semidirect
53. C2×#13063299C22semidirect
54. #121×D43C22semidirect
55. #14583379C22semidirect
56. #14583059C22semidirect
57. #14583058C22semidirect
58. #14583054C22semidirect
59. #14583049C22semidirect
60. #14583048C22semidirect
61. #14583046C22semidirect
62. #14583045C22semidirect
63. #14583045C22semidirect
64. #14583042C22semidirect
65. #14583041C22semidirect
66. #14583040C22semidirect
67. #14583037C22semidirect
68. #14583035C22semidirect
69. #14583034C22semidirect
70. #14583034C22semidirect
71. #14583033C22semidirect
72. #14583033C22semidirect
73. #14583033C22semidirect
74. #14583032C22semidirect
75. #14583031C22semidirect
76. #14582902C22semidirect
77. #14582901C22semidirect
78. #14582897C22semidirect
79. #14582893C22semidirect
80. #14582892C22semidirect
81. C2×#13063246C22semidirect
82. #102×D43C22semidirect
83. #14582867C22semidirect
84. #14582864C22semidirect
85. #14582861C22semidirect
86. C2×C22⋊(C43⋊C8)C22semidirect
87. C22⋊C8×D43C22semidirect
88. C23×D4×C43C22semidirect
89. C2×AGL(1,ℤ/8)×C43C22semidirect
90. C43×#525C22semidirect
91. C43×#450C22semidirect
92. C43×#450C22semidirect
93. C43×#447C22semidirect
94. C43×#447C22semidirect
95. C43×#418C22semidirect
96. C43×#407C22semidirect
107. #13063370D4semidirect
108. C2×#10621902C23semidirect
136. C22×D172C23semidirect
158. C2×D4×D43C23semidirect
167. C2×#10621885C23semidirect
168. C2×#10621873C23semidirect
169. C2×#10621883C23semidirect
170. C2×#10621884C23semidirect
171. C2×D344C23semidirect
173. C2×#10621882C23semidirect
174. C2×#10621882C23semidirect
175. C2×#10621882C23semidirect
178. C2×#10621872C23semidirect
179. C22×C43⋊C8C23semidirect
180. C2×C8×D43C23semidirect
188. #13063301C23semidirect
190. #13063300C23semidirect
191. #13063300C23semidirect
196. #13063299C23semidirect
202. #13063296C23semidirect
212. #13063283C23semidirect
213. C2×C4⋊Dic43C23semidirect
214. C4⋊C4×D43C23semidirect
217. #13063250C23semidirect
218. #13063248C23semidirect
219. #13063248C23semidirect
220. #13063247C23semidirect
221. #13063246C23semidirect
222. #13063246C23semidirect
223. #13063245C23semidirect
224. #13063245C23semidirect
227. C22⋊(C43⋊C8)C23semidirect
228. (C2×D43)⋊C8C23semidirect
229. (C2×D43)⋊C8C23semidirect
231. C2×#41×C43C23semidirect
241. C2×SD16×C43C23semidirect
242. C2×D8×C43C23semidirect
243. C2×M16×C43C23semidirect
246. C22⋊Q8×C43C23semidirect
248. #121×C43C23semidirect
252. #117×C43C23semidirect
253. #102×C43C23semidirect
254. #102×C43C23semidirect
256. C22⋊C8×C43C23semidirect
287. C2×D4×C43C2×D4semidirect
336. #10621900C2×D4semidirect
348. D4×D43C2×D4semidirect
361. #10621898C2×D4semidirect
567. C22×C43#576semidirect
608. #3003D43semidirect
642. C23×D4C2×D43semidirect
647. C2×AGL(1,ℤ/8)C2×D43semidirect
664. #525C2×D43semidirect
673. #450C2×D43semidirect
674. #450C2×D43semidirect
690. #447C2×D43semidirect
691. #447C2×D43semidirect
693. #418C2×D43semidirect
703. #407C2×D43semidirect
706. C43#60372semidirect
742. C2×#41C22×D43semidirect
792. C2×SD16C22×D43semidirect
799. C2×D8C22×D43semidirect
802. C2×M16C22×D43semidirect
815. C22⋊Q8C22×D43semidirect
831. #121C22×D43semidirect
845. #117C22×D43semidirect
858. #102C22×D43semidirect
859. #102C22×D43semidirect
866. C22⋊C8C22×D43semidirect
976. C2×D4D4×D43semidirect
1194. C22#14583703semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#130633702
C2×#145837032
#191482562
#191439002
#191438982
#191438642
#191438582
#191438492
#191438422
#191438232
#191438142
#191438112
C2×#145830332
#447×D432
#191431202
#191430452
C43×#30032
#6037243